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on Game Theory |
| By: | Philipp Külpmann; Davit Khantadze |
| Abstract: | In this paper, we use a laboratory experiment to investigate the effect of absence of common knowledge on the outcomes of coordination games. We introduce cognitive types into a pure coordination game in which there is no common knowledge about the distribution of cognitive types. In our experiment, around 76% of the subjects managed to coordinate on the payoff-dominant equilibrium despite the absence of common knowledge. However, around 9% of the players had first-order beliefs that lead to coordination failure and another 9% exhibited coordination failure due to higher-order beliefs. Furthermore, we compare our results with predictions of different models of higher-order beliefs, commonly used in the literature. |
| JEL: | C72 C92 D83 |
| Date: | 2016–11–21 |
| URL: | http://d.repec.org/n?u=RePEc:jmp:jm2016:pkl168&r=gth |
| By: | AJ Bostian (School of Social Sciences and Humanities, University of Tampere, Tampere, Finland); David Goldbaum (Economics Discipline Group, University of Technology, Sydney) |
| Abstract: | Crawford and Haller (1990) describe a repeated two-player coordination game defined by the absence of a common language. Coordination is achieved only through path dependent play relying on time consistent labels. We consider a game played by a large population similarly looking to coordinate but without the consistency in labels over time and with asymmetric coordinated payoff so that players have differing preferences regarding which coordinated structure emerges. In experiments, we link subjects together in a social network with limited ability to observe others. The complexity of the game and multitude of states thwarts solving for optimal play and yet the population demonstrates success in employing path dependency and the consistency of the social relationships to learn to coordinate. To capture this evolution, we model decisions with an experience-weighted attractor having recency, reinforcement, and lock-on biases. We find considerable heterogeneity in biases across individuals. Drawing on the observed biases, we conduct simulations to identify the extent to which individuals and environment determine group dynamics. |
| Keywords: | Experiment; Simulation; Social Network; Experience Weighted Attraction; Nested Logit |
| JEL: | C73 D83 D85 |
| Date: | 2016–04–11 |
| URL: | http://d.repec.org/n?u=RePEc:uts:ecowps:36&r=gth |
| By: | Csóka, Péter; Herings, Jean-Jacques P. |
| Abstract: | We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Since clearing payment matrices and the corresponding values of equity are not uniquely determined, we provide bounds on the possible levels equity can take. Unlike the existing literature, which studies centralized clearing procedures, we introduce a large class of decentralized clearing processes. We show the convergence of any such process in finitely many iterations to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure. |
| Keywords: | networks, bankruptcy problems, systemic risk, decentralized clearing, indivisibilities |
| JEL: | C71 G10 |
| Date: | 2016–11–03 |
| URL: | http://d.repec.org/n?u=RePEc:cvh:coecwp:2016/14&r=gth |
| By: | Joseph Abdou (Centre d'Economie de la Sorbonne); Nikolaos Pnevmatikos (Centre d'Economie de la Sorbonne) |
| Abstract: | We study the asymptotic value of a frequency-dependent zero-sum game following a differential approach. In such a game the stage payoffs depend on the current action and on the frequency of actions played so far. We associate in a natural way a differential game to the original game and although it presents an irregularity at the origin, we prove existence of the value on the time interval [0,1]. We conclude, using appropriate approximations, that the limit of Vn as n tends to infinity, exists and that it coincides with the value of the associated continuous time game |
| Keywords: | stochastic game; frequency dependent payoffs; continuous-time game; Hamilton-Jacobi-Bellman-Isaacs equation |
| JEL: | C73 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:16076&r=gth |
| By: | Pierre Bernhard (BIOCORE - Biological control of artificial ecosystems - INRA - Institut National de la Recherche Agronomique - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - LOV - Laboratoire d'océanographie de Villefranche - UPMC - Université Pierre et Marie Curie - Paris 6 - INSU - CNRS - Centre National de la Recherche Scientifique); Marc Deschamps (BETA - Bureau d'Economie Théorique et Appliquée - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique, GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis - CNRS - Centre National de la Recherche Scientifique, CRESE - Centre de REcherches sur les Stratégies Economiques - UFC - UFC - Université de Franche-Comté) |
| Abstract: | This note follows our previous works on games with randomly arriving players [3] and [5]. Contrary to these two articles, here we seek a dynamic equilibrium, using the tools of piecewise deterministic control systems The resulting discrete Isaacs equation obtained is rather involved. As usual, it yields an explicit algorithm in the finite horizon, linear-quadratic case via a kind of discrete Riccati equation. The infinite horizon problem is briefly considered. It seems to be manageable only if one limits the number of players present in the game. In that case, the linear quadratic problem seems solvable via essentially the same algorithm, although we have no convergence proof, but only very convincing numerical evidence. We extend the solution to more general entry processes, and more importantly , to cases where the players may leave the game, investigating several stochastic exit mechanisms. We then consider the continuous time case, with a Poisson arrival process. While the general Isaacs equation is as involved as in the discrete time case, the linear quadratic case is simpler, and, provided again that we bound the maximum number of players allowed in the game, it yields an explicit algorithm with a convergence proof to the solution of the infinite horizon case, subject to a condition reminiscent of that found in [20]. As in the discrete time case, we examine the case where players may leave the game, investigating several possible stochastic exit mechanisms. MSC: 91A25, 91A06, 91A20, 91A23, 91A50, 91A60, 49N10, 93E03. Foreword This report is a version of the article [2] where players minimize instead of maximizing, and the linear-quadratic examples are somewhat different. |
| Abstract: | On détermine les stratégies d'équilibre dans un jeu dynamique où des joueurs identiques arrivent de façon aléatoire, comme, par exemple, des congénères arrivant sur une même ressource. On considère aussi divers mécanismes de sortie aléatoire. On obtient des théorèmes d'existence et des algorithmes de calcul, plus explicites dans le cas particulier linéaire quadratique. Toute l'étude est conduite en horizon fini et en horizon infini, et en temps discret et en temps continu. Ce rapport est une version du working paper CRESE des mêmes auteurs (en économie mathématique), référence [2], mais où les joueurs minimisent au lieu de maximiser, et les exemples linéaires quadratiques sont un peu différents. |
| Keywords: | Nash equilibrium, Dynamic programming, Isaacs equation, Piecewise deterministic Markov decision processes |
| Date: | 2016–10–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01379644&r=gth |
| By: | Hassan Benchekroun (McGill University); Charles Figuières (Aix-Marseille University (Aix-Marseille School of Economics), CNRS, & EHESS); Mabel Tidball (INRA - LAMETA) |
| Abstract: | Our paper proposes an original angle to study the free-rider problem in the provision of public goods when the regulator has no information about agents' preferences. For a given outcome - specifically a Lindahl allocation - we ask what assumptions have to be imposed on simple mechanisms (in a precisely defined sense) that have the ability to Nash-implement it. Our answer lies in two main results: i) transfers necessarily belongs to a class of mechanisms that are linear in individual contributions to the public good, ii) there exists a subset of this class that fully implement Lindahl allocations. This subset encompasses, but does not reduce to, Walker (1981). |
| Keywords: | Lindahl allocations, mechanism design |
| JEL: | H41 C72 D62 D82 |
| Date: | 2016–10 |
| URL: | http://d.repec.org/n?u=RePEc:aim:wpaimx:1637&r=gth |
| By: | David Goldbaum (Economics Discipline Group, University of Technology, Sydney) |
| Abstract: | This paper examines network formation among a connected population with a preference for conformity and leadership. Agents build stable personal relationships to achieve coordinated actions. The network serves as a repository of collective experiences so that cooperation can emerge from simple, myopic, self-serving adaptation to recent events despite the competing impulses of conformity and leadership and despite limiting individuals to only local information. Computational analysis reveals how behavioral tendencies impact network formation and identifies locally stable disequilibrium structures. |
| Keywords: | Leader; Dynamic Network; Payoff interdependence; Social Interaction; Simulation |
| JEL: | D85 D71 C71 |
| Date: | 2016–04–29 |
| URL: | http://d.repec.org/n?u=RePEc:uts:ecowps:37&r=gth |
| By: | Martin Hellwig (Max Planck Institute for Research on Collective Goods) |
| Abstract: | Kolmogorov’s extension theorem provides a natural mapping from the space of coherent hierarchies of an agent’s first-order, second-order, etc. beliefs to the space of probability measures over the exogenous parameters and the other agents' belief hierarchies. Mertens and Zamir (1985) showed that, if the spaces of belief hierarchies are endowed with the product topology, then this mapping is a homeomorphism. This paper shows that this mapping is also a homeomorphism if the spaces of belief hierarchies are endowed with the uniform weak topology of Chen et al. (2010) or the universal strategic topology of Dekel et al. (2006), both of which ensure that strategic behaviour exhibits desirable continuity properties. |
| Keywords: | incomplete information, universal type space, uniform weak topology, uniform strategic topology, homeomorphism theorem |
| JEL: | C70 C72 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2016_17&r=gth |
| By: | Philippe Bich (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics); Rida Laraki (Ecole Polytechnique [Palaiseau]) |
| Abstract: | This paper studies the existence of equilibrium solution concepts in a large class of economic models with discontinuous payoff functions. The issue is well understood for Nash equilibria, thanks to Reny's better-reply security condition (Reny (1999)), and its recent improvements (Barelli and Meneghel (2013); McLennan et al. (2011); Reny (2009, 2011)). We propose new approaches, related to Reny's work, and obtain tight conditions for the existence of approximate equilibria and of sharing rule solutions in pure and mixed strategies (Simon and Zame (1990)). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that many competition models have a sharing rule solution. |
| Keywords: | timing games, strategic approximation,auctions,Discontinuous games, better-reply security, sharing rules,approximate equilibrium, Reny equilibrium |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-01396183&r=gth |
| By: | David P. Baron; Renee Bowen; Salvatore Nunnari |
| Abstract: | We present a laboratory experiment to study the effect of communication on durable coalitions – coalitions that support the same allocation from one period to the next. We study a bargaining setting where the status quo policy is determined by the policy implemented in the previous period. Our main experimental treatment is the opportunity for subjects to negotiate with one another through unrestricted cheap-talk communication before a proposal is made and comes to a vote. We compare committees with no communication, committees where communication is public and messages are observed by all committee members, and committees where communication is private and any committee member can send private messages to any other committee member. We find that the opportunity to communicate has a significant impact on outcomes and coalitions. When communication is public, there are more universal coalitions and fewer majoritarian coalitions. With private communication, there are more majoritarian coalitions and fewer universal coalitions. With either type of communication coalitions occur more frequently and last longer than with no communication. The content of communication is correlated with coalition type and with the formation and dissolution of durable coalitions. These findings suggest a coordination role for communication that varies with the mode of communication. |
| JEL: | C73 C78 C92 D71 D72 D78 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:22821&r=gth |
| By: | Matt Van Essen (Department of Economics, Finance and Legal Studies, University of Alabama); John Wooders (Economics Discipline Group, University of Technology, Sydney) |
| Abstract: | In financial disputes arising from divorce, inheritance, or the dissolution of a partnership, frequently the need arises to assign ownership of an indivisible item to one member of a group. This paper introduces and analyzes a dynamic auction for simply and efficiently allocating an item when participants are privately informed of their values. In the auction, the price rises continuously. A bidder who drops out of the auction, in return for surrendering his claim to the item, obtains compensation equal to the difference between the price at which he drops and the preceding drop price. When only one bidder remains, that bidder wins the item and pays the compensations of his rivals. We characterize the unique equilibrium with risk-neutral and CARA risk averse bidders. We show that dropout prices are decreasing as bidders become more risk averse. Each bidder’s equilibrium payoff is at least 1/N-th of his value for the item. Indeed, we show that each bidder’s security payoff is 1/N-th of his value. We introduce the notion of a perfect security strategy, we show that each bidder has a unique perfect security strategy, and that it coincides with the equilibrium bidding strategy as bidders becomes infinitely risk averse. |
| Date: | 2016–01–22 |
| URL: | http://d.repec.org/n?u=RePEc:uts:ecowps:32&r=gth |
| By: | Baron, David; Bowen, T. Renee; Nunnari, Salvatore |
| Abstract: | We present a laboratory experiment to study the effect of communication on durable coalitions - coalitions that support the same allocation from one period to the next. We study a bargaining setting where the status quo policy is determined by the policy implemented in the previous period. Our main experimental treatment is the opportunity for subjects to negotiate with one another through unrestricted cheap-talk communication before a proposal is made and comes to a vote. We compare committees with no communication, committees where communication is public and messages are observed by all committee members, and committees where communication is private and any committee member can send private messages to any other committee member. We find that the opportunity to communicate has a significant impact on outcomes and coalitions. When communication is public, there are more universal coalitions and fewer majoritarian coalitions. With private communication, there are more majoritarian coalitions and fewer universal coalitions. With either type of communication coalitions occur more frequently and last longer than with no communication. The content of communication is correlated with coalition type and with the formation and dissolution of durable coalitions. These findings suggest a coordination role for communication that varies with the mode of communication. |
| Keywords: | communication; Endogenous Status Quo; Laboratory experiments; legislative bargaining |
| JEL: | C73 C78 C92 D71 D72 D78 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11613&r=gth |
| By: | Angelo Antoci (University of Sassari, Italy); Simone Borghesi (University of Siena, Italy); Gianluca Iannucci (University of Florence, Italy) |
| Abstract: | This paper studies environmental corruption via a random matching evolutionary game between a population of firms and a population of bureaucrats who have to decide whether to release a “green” license to the firms. A firm obtains the license if the bureaucrat checks that it complies with environmental regulations, otherwise it is sanctioned. The model assumes that there are two types of bureaucrats (honest and dishonest), two types of firms (compliant and non-compliant), and two possible crimes (corruption and extortion). Corruption occurs when a dishonest bureaucrat accepts a bribe from a non-compliant firm, while extortion occurs when a dishonest bureaucrat claims a bribe from a compliant firm. When there is no dominance of strategies, we show that there exist two bistable regimes, in which two attractive stationary states exist, and two regimes with an internal stable equilibrium, corresponding to the mixed strategy Nash equilibrium of the one-shot static game, surrounded by closed trajectories. From comparative statics analysis performed on the latter two dynamic regimes, it emerges that policy instruments may help the Public Administration reduce both corruption and extortion, although increasing sanctions and detection probability do not always get the desired results. |
| Keywords: | Bureaucratic corruption, Evolutionary games, Environmental regulations, Economics of crime |
| JEL: | C73 D21 D73 K42 Q52 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:srt:wpaper:1016&r=gth |
| By: | Greiff, Matthias; Egbert, Henrik |
| Abstract: | This paper introduces the Pay-What-You-Want game which represents the interaction between a buyer and a seller in a Pay-What-You-Want (PWYW) situation. The PWYW game embeds the dictator game and the trust game as subgames. This allows us to use previous experimental studies with the dictator and the trust game to identify three factors that can influence the success of PWYW pricing in business practice: (i) social context, (ii) social information, and (iii) deservingness. Only few cases of PWYW pricing for a longer period of time have been documented. By addressing repeated games, we isolate two additional factors which are likely to contribute to successful implementations of PWYW as a long term pricing strategy. These are (iv) communication and (v) the reduction of goal conflicts. The central implication of this study is that the results from experimental economics can provide guidance to developing long-term applications of PWYW pricing. |
| Keywords: | Pay-What-You-Want; PWYW Game; participative pricing; experiments; reciprocity |
| JEL: | C90 D11 M21 M31 |
| Date: | 2016–11–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:75222&r=gth |
| By: | David Goldbaum (Economics Discipline Group, University of Technology, Sydney) |
| Abstract: | To better understand trends, this paper models the behavior of decision-makers seeking conformity and in fluence in a connected population. Link formation is one-sided with information flowing from the target to the link's originator. A premium for leading ensures that a link's target benefits more from the link than its originator, and yet a leader serves the population by coordinating decisions. The desire for conformity drives the population to organize into a single hub with the leader at the center. Certain conditions support multiple leader structures as Nash as well. A strong desire to infl uence produces an equilibrium with an unlinked subpopulation. |
| Keywords: | Opinion leadership; Social networks; Conformity; Non-cooperative games |
| JEL: | C72 D83 D85 |
| Date: | 2016–03–28 |
| URL: | http://d.repec.org/n?u=RePEc:uts:ecowps:35&r=gth |
| By: | Gao, Lin |
| Abstract: | This paper extends the concept of interaction platforms and explores the evolution of interaction and cooperation supported by individuals’ changing trust and trustworthiness on directed weighted regular ring network from the angle of micro scope by using agent-based modeling. This agent-based model integrates several considerations below via a relatively delicate experimental design: 1) a characteristic of trust is that trust is destroyed easily and built harder (Slovic, 1993); 2) trustworthiness may be reflected on both strategy decision and payoff structure decision; 3) individuals can decide whether or not to be involved in an interaction; 4) interaction density exists, not only between neighbors and strangers (Macy and Skvoretz, 1998), but also within neighbors; 5) information diffusion. In this agent-based model, marginal rate of exploitation of original payoff matrix and relative exploitation degree between two payoff matrices are stressed in their influence of trust-destroying; influence of observing is introduced via imagined strategy; relationship is maintained through relationship maintenance strength, and so on. This paper treats number of immediate neighbors, degree of embeddedness in social network, mutation probability of payoff matrix, mutated payoff matrix, proportion of high trust agents and probabilities of information diffusion within neighborhood and among non-neighbors as important aspects happening on interaction platforms, and the influences of these factors are probed respectively on the base of a base-line simulation. |
| Keywords: | Trust, trustworthiness, directed weighted regular ring network, agent-based modeling, marginal rate of exploitation, relative exploitation degree, imagined strategy, relationship maintenance strength, number of neighbors, degree of embeddedness in social network, mutation of payoff matrix, information diffusion, social mobility, institutional quality, evolution of interaction, evolution of cooperation |
| JEL: | B52 C63 D82 D85 |
| Date: | 2016–11–21 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:75214&r=gth |
| By: | John Asker; Chaim Fershtman; Jihye Jeon; Ariel Pakes |
| Abstract: | We investigate the impact of information sharing between rivals in a dynamic auction with asymmetric information. Firms bid in sequential auctions to obtain inputs. Their inventory of inputs, determined by the results of past auctions, are privately known state variables that determine bidding incentives. The model is analyzed numerically under different information sharing rules. The analysis uses the restricted experience based equilibrium concept of Fershtman and Pakes (2012) which we refine to mitigate multiplicity issues. We find that increased information about competitors’ states increases participation and inventories, as the firms are more able to avoid the intense competition in low inventory states. While average bids are lower, social welfare is unchanged and output is increased. Implications for the posture of antitrust regulation toward information sharing agreements are discussed. |
| JEL: | C63 C73 D43 K21 L41 |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:22836&r=gth |